What Is the Final Equilibrium Temperature Between Aluminum and Iron Blocks?

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    Thermodynamics
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Discussion Overview

The discussion revolves around determining the final equilibrium temperature between a 20 kg aluminum block at 200°C and a 20 kg iron block at 100°C. Participants explore the principles of heat transfer, energy conservation, and entropy change in a closed system, with a focus on the specific heat capacities of the materials involved.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant requests help in finding the final equilibrium temperature and total entropy change for the system.
  • Another participant suggests that the aluminum block will heat the iron block until their temperatures equalize, noting the different energy-temperature relationships for aluminum and iron.
  • A participant provides specific heat values and proposes a mathematical approach using the first law of thermodynamics and entropy equations, indicating that the system can be modeled as incompressible.
  • Further elaboration on the geometry of the blocks is introduced, discussing the contact surface and suggesting that the final temperature is reached at the contact surface before any heat transfer occurs through the volume of the blocks.

Areas of Agreement / Disagreement

Participants generally agree on the need to find the final equilibrium temperature and the use of specific heat capacities in the calculations. However, there are multiple approaches and models proposed, and the discussion remains unresolved regarding the exact final temperature and the implications of the geometry of the blocks.

Contextual Notes

Participants have not fully defined all assumptions, such as the contact surface area and the implications of cylindrical symmetry. The discussion includes unresolved mathematical steps and dependencies on specific definitions of heat transfer and system boundaries.

needy
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a 20 Kg Aluminum block initially at 200 C is brought into contact with a 20 Kg block of Iron at 100 C. I need the final equilibrium temperature and the total entropy change for this process.

I have an idea on how to find the chango of entropy, what I'm struggling with is finding the final temperature.

Help Please
 
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Hi needy, welcome to PF. If this is a homework question, it's probably going to be moved. Also, you should discuss what equations you've found and tried so far so we know where to start.

You've probably figured out that the Al block is going to heat the Fe block until the temperatures are equal. But the relationship between energy and temperature is different between Al and Fe. Have you gotten this far?
 
Specific heat of aluminium =0,88 J / kg K.
Define temperature of the iron block as zero how much energy has the aluminium to divide over the aluminium- and iron block together.
 
needy said:
a 20 Kg Aluminum block initially at 200 C is brought into contact with a 20 Kg block of Iron at 100 C. I need the final equilibrium temperature and the total entropy change for this process.

I have an idea on how to find the change of entropy, what I'm struggling with is finding the final temperature.

Help Please

Closed system, control mass.

What you're going to want to do is model both objects as incompressible.
ca=specific heat aluminum
ci=specific heat iron
m=mass
Tf=temp final
Ti=temp Fe
Ta=temp Al

Imcompressible 1st Law
U=Q-W Q=0, W=0
U=0
U=m*c*(T2-T1)
so
Ui+Ua=0
then
mi*ci*(Tf-Ti)+ma*ca*(Tf-Ta)=0

For incompressible substances, Change in S (entropy) is S= m*c*(ln(T2/T1))

Your second law equation is of course S2-S1=Q/T+o(entropy production) Q/T=0 (no boundary heat loss)

so S2-S1=o (Treat S2-S1 as change in S)

mi*ci*ln(Tf/Ti)+ma*ca*ln(Tf/Ta)=o

Double check for any typing errors, etc.
Hope that helps!
 
Last edited:
Ok the system is almost fully defined. What is needed is the contact surface O, and Needy I hope that you agree in cilindersymmetry. Then there are to heights hi and ha.
So the volume of aluminium block Va=O*ha and for the Ferro block: Vi=O*hi. Then we can define de temperature on the line -ha<= x <=+hi, in which the point x=0 means a point on the contact surface. It is logical to hypothesize that the final state Tf is reached there first, and that at that moment no heat-transport trough O takes place.
At that moment the two blocks can be separated and calculated how the remaining heattransfer takes place in them
 

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